(1) Norges Tekniske Høgskole, Institutt for Numerisk Matematik, Universitetet i Trondheim, N-7034 Trondheim, Norge;(2) Department of Computer Sciences, Chalmers University of Technology, Fack, S-402 20 Göteborg 5, Sweden
Abstract:
Summary Based on the theory of Butcher series this paper developes the order conditions for Rosenbrock methods and its extensions to Runge-Kutta methods with exact Jacobian dependent coefficients. As an application a third order modified Rosenbrock method with local error estimate is constructed and tested on some examples.